Linear Method Research Articles

Equivalent continuous method based novel design of a nonlinear TMD with piecewise stiffness

Tuned mass Dampers (TMDs) are extensively used passive control devices for high-rise buildings to mitigate undesirable responses. In practice, limit devices are frequently applied due to the large displacement of TMD, resulting in the emergence of piecewise nonlinearity. In this study, a TMD with piecewise stiffness (PSTMD) is developed to investigate the piecewise nonlinearity, including piecewise linear stiffness (PLS) and piecewise nonlinear stiffness (PNS). Initially, a novel equivalent continuous method (ECM) is proposed based on the principles of the least squares method (LSM) to approximate the PSTMD using a nonlinear TMD with Duffing stiffness. The equivalent nonlinear TMD is proven to be accurate enough to approximate the PSTMD. Subsequently, frequency response analysis is conducted on the PSTMD designed by linear method, results indicate that the linear method fails to design PSTMD. Thirdly, the optimal parameters of PSTMD are determined based on the ECM and the improved design method for nonlinear TMD proposed by the author. Results indicate that this novel design method effectively enhances the performance of PSTMD and mitigates the effect of piecewise nonlinearity. Finally, the influence of parameters of PSTMD on the optimal tuning frequency is investigated. The influence of damping ratio of PSTMD is explored by numerical simulation, with results indicating that employing the damping ratio suggested by traditional linear design method as the optimal parameter is reasonable. In summary, the novel method proposed in this study holds significance for the engineering design of TMDs with piecewise characteristics.

A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection

A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection

Hyperspectral remote sensing of forage stoichiometric ratios in the senescent stage of alpine grasslands

Senescence is an important phenological stage in the life cycle of grassland plants, and estimating grass senescence in alpine grasslands is particularly crucial for animal husbandry and grazing the utilization of grassland resources for grazing. However, the application of proximal sensing technologies to capture the variations in forage growth parameters in the senescent stage, especially regarding some key stoichiometric ratios, still faces challenges associated with indiscernible spectral properties and indeterminate absorption and reflectance features. The present study aims to demonstrate the potential and effectiveness of applying hyperspectral data to assess the forage carbon-nitrogen (C:N) ratio and calcium-phosphorus (Ca:P) ratio during the senescent stage (September to November). A progressive variable dimensionality reduction strategy based on a genetic algorithm (GA) and hybrid optimization method (ant optimization colony (ACO) and extreme learning machine (ELM)) coupled with multiple linear and nonlinear statistical methods is applied to develop C:N ratio and Ca:P ratio estimation models via combination with data from 205 sample sites collected from six field campaigns (2016-2019) on the eastern Tibetan Plateau. The results show that the important spectral bands favorable for forage C:N ratio and Ca:P ratio retrieval are generally in the red and shortwave infrared (SWIR) regions, and the proposed model presents satisfactory performance in the estimation of the forage C:N ratio (V-R2 = 0.81, V-RMSE = 6.44) and Ca:P ratio (V-R2 = 0.64, V-RMSE = 2.54) during senescence. Moreover, the model can effectively overcome the spatial differences among sampling areas and perform optimally in capturing the variations in the forage C:N ratio and Ca:P ratio in the early and middle stages of senescence. Overall, our study demonstrates that it is feasible and promising to estimate these stoichiometric ratios using hyperspectral feature bands during grass senescence at the canopy level, with potential applications that may further enhance the monitoring of forage quality and quantity.

Water quality evaluation based on water quality index and multiple linear regression: A research on Hanyuan Lake in southern Sichuan Province, China.

This study aims to understand the changes in the water quality of Hanyuan Lake and to show these changes over time. In this study, monthly sampling was conducted at three sampling sites in Hanyuan Lake, and water samples were measured for water quality indicators in the laboratory according to the methods specified in the Environmental Quality Standards for Surface Water (GB3838-2002). Based on the monitoring data from January to December 2019, the WQI comprehensive evaluation method was used to conduct multiple linear stepwise regression analysis, extract key indicators, and establish the WQImin model. The results show that according to the WQI comprehensive evaluation method, the WQI values of Hanyuan Lake are all above 90, and the grade is excellent. The overall water quality of Hanyuan Lake is excellent, and most of the water quality indexes reach the Class I standard in the Environmental Quality Standards for Surface Water (GB3838-2002). WQImin1 (R2 = 0.86, p < 0.001, PE = 4.28) as the best WQImin model. In this study, a model with fewer parameters was established by multiple linear regression method, which is conducive to better monitoring of water quality at monitoring stations while saving costs. PRACTITIONER POINTS: According to the WQI comprehensive evaluation method, the WQI values of Hanyuan Lake are all above 90, the rating is excellent. From January 2019 to September 2020, the monthly change trend of each section is roughly the same, showing a trend of first decreasing, then rising, then decreasing, and finally rising and flattening. The WQImin model was developed to completely describe the change in the water body.

Reconstruction of Mixed Boundary Objects and Classification Using Deep Learning and Linear Sampling Method

Reconstruction of Mixed Boundary Objects and Classification Using Deep Learning and Linear Sampling Method

Comparative Analysis of Framed-Tube &amp; Braced-Tube System in Tall Buildings Using ETABS

Abstract: Since the rigid frame became popular in the first half of the 20th century, tall buildings with structural systems have evolved. The development of underlying frameworks for tall structures lays on reasonable realism, economy of material utilization, effortlessness and polish, and worry for constructability. We are now able to build buildings that are ever higher thanks to cutting-edge building materials, sophisticated computational software, and sturdy structural systems. The rationale behind the creation of structural systems for tall buildings is to achieve architectural expression, ensure safety and serviceability, and make rational and effective use of materials. The use of composite structures, which combine the advantages of various materials, has been the trend in structural systems for tall buildings. In both static and dynamic conditions, these high-rise structures ought to be able to withstand a variety of lateral loads, such as wind load and earthquake load. This study examines the responses of the Framed Tube, Braced Tube, structural systems to various parameters such as Story displacement, Story drift, Story shear, and time period. The analysis focuses on 60-story structures situated in Seismic Zone III with medium soil conditions. The static analysis of the structures is conducted using the linear static method, which involves wind load calculations using the force coefficient method. On the other hand, the dynamic analysis is performed using the response spectrum method, with wind load calculations carried out using the gust factor calculation method.

Establishment of Linear Stability Analysis Method of Hypersonic Boundary Layer Reflecting Porous Surface Effect

Establishment of Linear Stability Analysis Method of Hypersonic Boundary Layer Reflecting Porous Surface Effect

Predicting anti-trypanosome effect of carbazole-derived compounds by powerful SVM with novel kernel function and comprehensive learning PSO.

In order to predict the anti-trypanosome effect of carbazole-derived compounds by quantitative structure-activity relationship, five models were established by the linear method, random forest, radial basis kernel function support vector machine, linear combination mix-kernel function support vector machine, and nonlinear combination mix-kernel function support vector machine (NLMIX-SVM). The heuristic method and optimized CatBoost were used to select two different key descriptor sets for building linear and nonlinear models, respectively. Hyperparameters in all nonlinear models were optimized by comprehensive learning particle swarm optimization with low complexity and fast convergence. Furthermore, the models' robustness and reliability underwent rigorous assessment using fivefold and leave-one-out cross-validation, y-randomization, and statistics including concordance correlation coefficient (CCC), [Formula: see text] , [Formula: see text] , and [Formula: see text] . Among all the models, the NLMIX-SVM model, which was established by support vector regression using a nonlinear combination of radial basis kernel function, sigmoid kernel function, and linear kernel function as a new kernel function, demonstrated excellent learning and generalization abilities as well as robustness: [Formula: see text] = 0.9581, mean square error (MSE) = 0.0199 for the training set and [Formula: see text] = 0.9528, MSE = 0.0174 for the test set. [Formula: see text] , [Formula: see text] , CCC, [Formula: see text] , [Formula: see text], and [Formula: see text] are 0.9539, 0.8908, 0.9752, 0.9529, 0.9528, and 0.9633, respectively. The NLMIX-SVM method proved to be a promising way in quantitative structure-activity relationship research. In addition, molecular docking experiments were conducted to analyze the properties of new derivatives, and a new potential candidate drug molecule was ultimately found. In summary, this study will provide help for the design and screening of novel anti-trypanosome drugs.

Influence of Capital Structure and Profitability on The Company Value of PT. Waskita Karya (Persero), TBK (Period 2016 To 2020)

This study focuses on the specific time period of 2016-2020 and aims to ascertain and examine the impact of capital structure and profitability on the valuation of manufacturing companies listed on the Indonesia Stock Exchange. The independent variable X1 represents the capital structure, precisely measured by the debt-equity ratio (DER). The independent variable is the company PT. Waskita Karya (Persero), Tbk, a prominent manufacturing company, throughout the period of 2016-2020. The study population consisted of 12 years' worth of financial reports from PT Waskita Karya (Persero), Tbk, encompassing quarters 1-4. This totaled 48 financial reports. The sample for analysis was selected using the time series approach, resulting in 20 financial reports from 2016 to 2020. The data testing strategy employs several linear regression analysis methods, utilizing an alpha significance level of 5%. The findings of this study demonstrate that the capital structure has a notable adverse impact on the firm's value, reducing it by 22.4%. Conversely, profitability substantially positively influences the company's value, increasing it by 30.8%. Both capital structure and profitability have a 53.2% impact on firm value at the same time.

Global Conditions and Changes in the Level of Renewable Energy Sources

The progressing globalization of the contemporary economy impacts its volatility and unpredictability. The directions of changes in the socioeconomic development of the contemporary global economy are determined by a number of interrelated diverse factors. Factors clearly influencing the development of the modern international economy include innovation, digitization processes, instability of the economy caused by armed conflicts or pandemic outbreaks, the concept of sustainable development, climate policy, as well as issues related to the depletion of energy resources and the necessity of ensuring global energy security. The purpose of the article is to identify the factors of the development of the contemporary economy along with the analysis and evaluation of their impacts on changes in the level of renewable energy sources (RESs) in the EU countries. The time scope of the analysis covers the years 2013 and 2022 (a 10-year perspective). The study used the methods of literature study, literature criticism, statistical data analysis (statistical databases: EUROSTAT and IRENA), and linear ordering methods (TOPSIS and EDAS). The study results indicate that the levels of the RESs have changed in response to the factors diagnosed in the study. In the years studied, the leaders in terms of levels of RES development were France, Spain, and Denmark.

Private Firm Valuation Using Multiples: Can Artificial Intelligence Algorithms Learn Better Peer Groups?

Forming optimal peer groups is a crucial step in multiplier valuation. Among others, the traditional regression methodology requires the definition of the optimal set of peer selection criteria and the optimal size of the peer group a priori. Since there exists no universally applicable set of closed and complementary rules on selection criteria due to the complexity and the diverse nature of firms, this research exclusively examines unlisted companies, rendering direct comparisons with existing studies impractical. To address this, we developed a bespoke benchmark model through rigorous regression analysis. Our aim was to juxtapose its outcomes with our unique approach, enriching the understanding of unlisted company transaction dynamics. To stretch the performance of the linear regression method to the maximum, various datasets on selection criteria (full as well as F- and NCA-optimized) were employed. Using a sample of over 20,000 private firm transactions, model performance was evaluated employing multiplier prediction error measures (emphasizing bias and accuracy) as well as prediction superiority directly. Emphasizing five enterprise and equity value multiples, the results allow for the overall conclusion that the self-organizing map algorithm outperforms the traditional linear regression model in both minimizing the valuation error as measured by the multiplier prediction error measures as well as in direct prediction superiority. Consequently, the machine learning methodology offers a promising way to improve peer selection in private firm multiplier valuation.

Trends in intraseasonal temperature variability in Europe: Comparison of station data with gridded data and reanalyses

AbstractTrends in temperature variability are often referred to have higher effect on temperature extremes than trends in the mean. We investigate trends in three complementary measures of intraseasonal temperature variability: (a) standard deviation of mean daily temperature (SD), (b) mean absolute value of day‐to‐day temperature change (DTD) and (c) 1‐day lagged temporal autocorrelation of temperature (LAG). It is a well‐established fact that different types of data (station, gridded, reanalyses) provide different temperature characteristics and particularly their trends. Moreover, we have uncovered that trends in measures of variability are considerably sensitive to data inhomogeneities. Therefore, we use five different datasets, one station based (ECA&amp;D), one gridded (EOBS) and three reanalyses (JRA‐55, NCEP/NCAR, 20CR), and compare them. The period from 1961 to 2014 where all datasets overlap is examined, and the linear regression method is utilized to calculate trends of investigated measures in summer and winter. Intraseasonal temperature variability tends to decrease in winter, especially in eastern and northern Europe, where trends below −7%·decade−1 are detected for all measures. Decreases in DTD and LAG (indicating increase in persistence) prevail also in summer while summer SD tends to increase. The increase in the width of temperature distribution and the simultaneous increase in persistence indicate a tendency towards the rise in the frequency of extended extreme events in summer. Unlike previous studies, our results imply that reanalyses are not the least accurate in determining trends. JRA‐55 appears to be the least diverging from other datasets, while the largest discrepancies are detected for DTD at station data.

Layered Fusion Reconstruction Based on Fuzzy Features for Multi-Conductivity Electrical Impedance Tomography

In medical imaging, detecting tissue anomalies is vital for accurate diagnosis and effective treatment. Electrical impedance tomography (EIT) is a non-invasive technique that monitors the changes in electrical conductivity within tissues in real time. However, the current challenge lies in simply and accurately reconstructing multi-conductivity distributions. This paper introduces a layered fusion framework for EIT to enhance imaging in multi-conductivity scenarios. The method begins with pre-imaging and extracts the main object from the fuzzy image to form one layer. Then, the voltage difference in the other layer, where the local anomaly is located, is estimated. Finally, the corresponding conductivity distribution is established, and multiple layers are fused to reconstruct the multi-conductivity distribution. The simulation and experimental results demonstrate that compared to traditional methods, the proposed method significantly improves multi-conductivity separation, precise anomaly localization, and robustness without adding uncertain parameters. Notably, the proposed method has demonstrated exceptional accuracy in local anomaly detection, with positional errors as low as 1% and size errors as low as 33%, which significantly outperforms the traditional method with respective minimum errors of 9% and 228%. This method ensures a balance between the simplicity and accuracy of the algorithm. At the same time, it breaks the constraints of traditional linear methods, struggling to identify multi-conductivity distributions, thereby providing new perspectives for clinical EIT.

Adaptive event-triggered optimal [formula omitted] tracking control for uncertain nonlinear systems: Comparative analysis applied to autonomic tractor-trailer system

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method.

Ecological niche modelling of Culicoides imicola and future range shifts under climate change scenarios in Italy.

Culicoides imicola is the main vector of viral diseases of livestock in Europe such as bluetongue (BT), African horse sickness and epizootic haemorrhagic disease. Climatic factors are the main drivers of C. imicola occurrence and its distribution might be subject to rapid shifts due to climate change. Entomological data, collected during BT surveillance, and climatic/environmental variables were used to analyse ecological niche and to model C. imicola distribution and possible future range shifts in Italy. An ensemble technique was used to weigh the performance of machine learning, linear and profile methods. Updated future climate projections from the latest phase of the Climate Model Intercomparison Project were used to generate future distributions for the next three 20-year periods, according to combinations of general circulation models and shared socioeconomic pathways and considering different climate change scenarios. Results indicated the minimum temperature of the coldest month (BIO 6) and precipitation of the driest-warmest months (BIO 14) as the main limiting climatic factors. Indeed, BIO 6 and BIO 14 reported the two highest values of variable importance, respectively, 9.16% (confidence interval [CI] = 7.99%-10.32%), and 2.01% (CI = 1.57%-2.44%). Under the worst-case scenario of climate change, C. imicola range is expected to expand northward and shift away from the coasts of central Italy, while in some areas of southern Italy, environmental suitability will decrease. Our results provide predictions of C. imicola distribution according to the most up-to-date future climate projections and should be of great use to surveillance management at regional and national scales.

#1227 The role of P-selectin (CD62P) expression in renal tissue in the development of diabetic nephropathy

Abstract Background and Aims The prevalence of diabetic nephropathy (DN) is increasing in line with the increase in the incidence of diabetes mellitus (DM) worldwide. The latest data from the International Diabetes Federation (IDF) predicts that by 2045, more than 10.5% of adults worldwide will have diabetes. This will lead to kidney damage in 100-250 million people. DN is characterized by structural and functional changes. As a result of chronic hyperglycemia, pathogenic changes in the vascular wall develop, and the frequency of micro- and macrovascular complications associated with morbidity and mortality among patients with diabetes increases. However, the exact mechanism of vascular complications is not completely clear. Endothelial dysfunction plays a key role in triggering the development of inflammatory mechanisms that are associated with vascular complications in patients with type 2 diabetes mellitus (T2DM). Activation of the endothelium due to increased release of cytokines and expression of adhesion molecules promotes platelet activation and their adhesion to the activated endothelium. Selectins (E-selectin, L-selectin and P-selectin) play a major role in the development of microvascular complications. The aim of the study was to examine the role of P-selectin (CD62p) expression in the glomerular endothelium and peritubular capillaries in patients with different morphological classes of DN and to evaluate its effect on the development and progression of morphological changes in renal tissue. Method Was examined 49 patients with T2DM complicated by the development of DN. The average age of the patients was 66.58 ± 3.27 years. There were 35 women, 14 men. The duration of the disease was 17.70 ± 0.35 years. The duration of DN from the moment of detection of microalbuminuria to the morphological examination of the renal tissue and diagnosis was 1.65 ± 0.34 years. All patients underwent light and immunofluorescence microscopy of kidney tissue biopsies obtained by intravital puncture biopsy. Morphological changes in tissue were assessed in accordance with the latest international classification of diabetic nephropathy developed by the Scientific Committee of the Pathology Society, USA. According to light microscopy data, class IIa (mild mesangial expansion) was detected in 12 patients, class IIb (severe mesangial expansion) in 14 patients, class III (Kimmelstil–Wilson nodular lesions) in 19 patients, and class IV (advanced diabetic glomerulosclerosis) in 5 patients. In addition to light microscopy, the expression of CD62β (P-selectin) in the glomerular endothelium and in peritubular capillaries was determined in all patients. FITc-labeled monoclonal antibodies (FITC anti-human CD62p Antibody, clone AK4 Cat#304904), were used (Biolegend, USA). Results Analysis of biopsy tissue from DN patients showed that CD62p expression is detected both in the glomerular endothelium (1.6383 ± 0.4789 (95% CI: 0.9574-2.7234)) and in peritubular capillaries (1.1702 ± 0.1308 (95% CI: 0.9149–1.4250)). Using the linear regression method with the calculation of the coefficients of determination R2 (R Square), the values of the F criterion, significant regression models were obtained: Expression of CD62p in the glomerular endothelium promotes the development and progression of arteriolar hyalinosis (R2=0.213, F=12.476 p=0.001); expansion of the mesangial matrix (R2=0.362, F=26.09, p=0.0001); thickening of the basement membrane (R2=0.127, F=6.57, p=0.014); development and progression of nodular Kimmelstiel–Wilson lesions (R2=0.106, F=5.360, p=0.025). Expression of CD62p in peritubular capillaries promotes the development of interstitial sclerosis (R2=0.549, F=54.732, p=0.0001). The severity of CD62p expression in the glomerular endothelium depends on the morphological class of DN in patients (R2=0.216, F=12.684, p=0.001). Conclusion

EEG entropy insights in the context of physiological aging and Alzheimer's and Parkinson's diseases: a comprehensive review.

In recent decades, entropy measures have gained prominence in neuroscience due to the nonlinear behaviour exhibited by neural systems. This rationale justifies the application of methods from the theory of nonlinear dynamics to cerebral activity, aiming to detect and quantify its variability more effectively. In the context of electroencephalogram (EEG) signals, entropy analysis offers valuable insights into the complexity and irregularity of electromagnetic brain activity. By moving beyond linear analyses, entropy measures provide a deeper understanding of neural dynamics, particularly pertinent in elucidating the mechanisms underlying brain aging and various acute/chronic-progressive neurological disorders. Indeed, various pathologies can disrupt nonlinear structuring in neural activity, which may remain undetected by linear methods such as power spectral analysis. Consequently, the utilization of nonlinear tools, including entropy analysis, becomes crucial for capturing these alterations. To establish the relevance of entropy analysis and its potential to discern between physiological and pathological conditions, this review discusses its diverse applications in studying healthy brain aging and neurodegenerative diseases, including Alzheimer's disease (AD) and Parkinson's disease (PD). Various entropy parameters, such as approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE), and permutation entropy (PermEn), are analysed within this context. By quantifying the complexity and irregularity of EEG signals, entropy analysis may serve as a valuable biomarker for early diagnosis, treatment monitoring, and disease management. Such insights offer clinicians crucial information for devising personalized treatment and rehabilitation plans tailored to individual patients.

Human Detection in Flood Using Drone

Drowning people in India approximately around 38000 peoples per year leads to dead finally because of, we have insufficient water rescue or timely emergency response to search and rescue team during emergency, also the lack of information to the rescue team about the drowning people place. We should believe that a few seconds' difference could have saved a person’s life. The timely information conveyed to the rescue team is also an important criterion for drowning to dead rate being very higher At first, we make a dataset, which contains many human targets at sea. Then, we improve the algorithm In the feature extraction network, we use the residual module with channel attention mechanism. Finally, on the settings of the raspberry pi Pico with GPS and GSM, we use a linear transformation method to deal with the python generated by clustering algorithm. The detection accuracy of the improved algorithm for human targets at sea is improved, which has a good detection effect. The drone with detecting and alerting with voice message to the Rescue Team at remote end with required all details about the drowning people make sense for faster rescue and save as the highest accuracy. The camera detection of the rescue Drone had a proper in that the range of the active camera and the speed of the video with Wi-Fi to the control room also optimal for the detection to work properly.

Technical note: Capturing shape-Linear measurements and geometric morphometrics of the immature femora.

Growth and developmental studies have been a prominent theme in bioarchaeology. These works traditionally focus on metric measurements of long bone length and age-at-death or cross-sectional geometric studies with the use of computed tomography scans for questions on growth and mobility. However, teasing apart aspects of size and shape have been difficult due to the cylindrical nature of immature long bones. This research investigates the methodological use of surface geometries from linear measurements and geometric morphometric methods (GMM) to answer questions on mobility and allometry during childhood. Left femora were selected from 42 individuals ranging from fetal to 12 years of age from medieval St Gregory's Priory, Canterbury, UK. Femora were digitized with structured-light-scanning for auto3dgm analysis and measurements were obtained from physical caliper measurements. Individuals were put into age groups based on biomechanical milestones during this age range. Ratio and GMM confirm hypotheses of allometry and biomechanical milestones. Geometric morphometrics, however, detects more subtle differences in mobility at each age group. The findings of this preliminary study support the potential use of GMM of immature femora, while indicating that the extent in range of mobility that can occur varies at different biological milestones.

Determinants of Marketing of Handloom Products Across Heterogeneous Weaving Business Units: A Study of Rural Assam

Success in marketing plays an important role in the growth and extension of rural non-farm informal sectors. The present study made an attempt to understand the marketing success among diverse groups of handloom weaving business units and factors determining the marketing of handloom products through the lens of weaving business units in rural Assam. Besides descriptive and inferential statistics, multiple linear regression method was applied for the analysis of data. The results of the study show that the success of marketing in terms of sales volume and revenue was significantly higher among the master weavers. Factors like years of schooling of handloom weaving entrepreneurs, business experience, working hours, storage capacity, advance payment requirement, number of handloom competitors in village, transportation cost, communication expense, and proximity to market significantly influenced the marketing across heterogeneous weaving business units in the study area. Steps towards the improvement of rural market infrastructure and road connectivity by taking a slew of suitable policies by Central and state governments may allow the rural handloom weavers to get better access to the market, which in turn, may assist in the promotion of sales.